Re: Can the radius be found?

Hi tmoria! :)

You do have a constraint.

Since the segments a, b, and c are in the same plane and bounded by 2 lines, you get the constraint: a-2b+c=0.

So let's suppose that a and b are known, then we require that:

$\displaystyle c=2b-a \qquad (1)$

Let's call the unnamed line segments A, B, and C.

Then we can set up the system of equations:

$\displaystyle A-2B+C=0$

$\displaystyle A^2+a^2=R^2$

$\displaystyle B^2+b^2=(R+d)^2$

$\displaystyle C^2+c^2=(R+2d)^2$

We have 4 equations with 5 unknowns.

That means we can choose one unknown for free.

So let's pick A ourselves, then we can solve the system getting:

$\displaystyle R=\sqrt{a^2 + A^2}$

$\displaystyle d=\frac{b-a}{a}R$

$\displaystyle B=\frac b a A$

$\displaystyle C=\frac c a A$

A solution like this is easiest to calculate with Wolfram|Alpha.

Re: Can the radius be found?

Quote:

Originally Posted by

**ILikeSerena**

...Since the segments a, b, and c are in the same plane and bounded by 2 lines..., you get the constraint: a-2b+c=0.

Hi ILikeSerena,

Many thanks for the effort you put in. Unfortunately I forgot to delete the two lines at the end of the segments as they are not straight lines, but slightly curved which does not show in the image. The amended image is included below. I apologize for you wasting your time :(

Lines MN and OP are straight.

http://i1307.photobucket.com/albums/...pse640f131.jpg